diff options
Diffstat (limited to 'Precond.agda')
| -rw-r--r-- | Precond.agda | 39 |
1 files changed, 20 insertions, 19 deletions
diff --git a/Precond.agda b/Precond.agda index a76fddc..bc54cd5 100644 --- a/Precond.agda +++ b/Precond.agda @@ -25,6 +25,7 @@ open import Relation.Binary.PropositionalEquality using (refl ; cong ; inspect ; open Relation.Binary.PropositionalEquality.≡-Reasoning using (begin_ ; _≡⟨_⟩_ ; _∎) open import Relation.Nullary using (yes ; no) +open import Structures using (IsFunctor) open import FinMap using (FinMapMaybe ; lookupM ; union ; fromFunc ; empty ; insert ; lemma-lookupM-empty ; delete-many ; lemma-tabulate-∘ ; delete ; lemma-lookupM-delete ; lemma-lookupM-fromFunc ; reshape ; lemma-reshape-id) import CheckInsert open CheckInsert (decSetoid deq) using (checkInsert ; lemma-checkInsert-new ; lemma-lookupM-checkInsert-other) @@ -32,8 +33,8 @@ import BFF import Bidir open Bidir (decSetoid deq) using (_in-domain-of_ ; lemma-assoc-domain) import GetTypes -open GetTypes.PartialVecVec using (Get ; module Get) -open BFF.PartialVecBFF (decSetoid deq) using (assoc ; enumerate ; denumerate ; bff ; enumeratel) +open GetTypes.PartialShapeVec using (Get ; module Get) +open BFF.PartialShapeBFF (decSetoid deq) using (assoc ; enumerate ; denumerate ; bff) lemma-maybe-just : {A : Set} → (a : A) → (ma : Maybe A) → maybe′ Maybe.just (just a) ma ≡ Maybe.just (maybe′ id a ma) lemma-maybe-just a (just x) = refl @@ -62,31 +63,31 @@ lemma-union-delete-fromFunc {n = n} {is = i ∷ is} {h = h} {g = g} (Data.List.A maybe′ just (lookupM i (delete-many is (fromFunc g))) (lookup i h) ∎ inner f | no f≢i = cong (flip (maybe′ just) (lookup f h)) (lemma-lookupM-delete (delete-many is (fromFunc g)) f≢i) -assoc-enough : (G : Get) → {i : Get.|I| G} → (j : Get.|I| G) → (s : Vec Carrier (Get.|gl₁| G i)) → (v : Vec Carrier (Get.|gl₂| G j)) → ∃ (λ h → assoc (Get.get G (enumeratel (Get.|gl₁| G j))) v ≡ just h) → ∃ λ u → bff G j s v ≡ just u -assoc-enough G {i} j s v (h , p) = _ , cong (_<$>_ (flip map t ∘ flip lookupM) ∘ _<$>_ (flip union (reshape g′ (|gl₁| j)))) p +assoc-enough : (G : Get) → {i : Get.|I| G} → (j : Get.|I| G) → (s : Get.Container G Carrier (Get.|gl₁| G i)) → (v : Vec Carrier (Get.|gl₂| G j)) → ∃ (λ h → assoc (Get.get G (enumerate (Get.ShapeT G) (Get.|gl₁| G j))) v ≡ just h) → ∃ λ u → bff G j s v ≡ just u +assoc-enough G {i} j s v (h , p) = _ , cong (_<$>_ ((λ f → fmap f t) ∘ flip lookupM) ∘ _<$>_ (flip union (reshape g′ (arity (|gl₁| j))))) p where open Get G - g′ = delete-many (get (enumerate s)) (fromFunc (denumerate s)) - t = enumeratel (|gl₁| j) + g′ = delete-many (get (enumerate ShapeT (|gl₁| i))) (fromFunc (denumerate ShapeT s)) + t = enumerate ShapeT (|gl₁| j) -assoc-enough′ : (G : Get) → {i : Get.|I| G} → (s : Vec Carrier (Get.|gl₁| G i)) → (v : Vec Carrier (Get.|gl₂| G i)) → ∃ (λ h → assoc (Get.get G (enumeratel (Get.|gl₁| G i))) v ≡ just h) → ∃ λ u → bff G i s v ≡ just (map just u) +assoc-enough′ : (G : Get) → {i : Get.|I| G} → (s : Get.Container G Carrier (Get.|gl₁| G i)) → (v : Vec Carrier (Get.|gl₂| G i)) → ∃ (λ h → assoc (Get.get G (enumerate (Get.ShapeT G) (Get.|gl₁| G i))) v ≡ just h) → ∃ λ u → bff G i s v ≡ just (Get.fmap G just u) assoc-enough′ G {i} s v (h , p) = _ , (begin bff G i s v ≡⟨ proj₂ (assoc-enough G i s v (h , p)) ⟩ - just (map (flip lookupM (union h (reshape g′ (|gl₁| i)))) t) + just (fmap (flip lookupM (union h (reshape g′ (arity (|gl₁| i))))) t) ≡⟨ cong just (begin _ - ≡⟨ cong (flip map t ∘ flip lookupM ∘ union h) (lemma-reshape-id g′) ⟩ - map (flip lookupM (union h g′)) t - ≡⟨ cong (flip map t ∘ flip lookupM) (proj₂ wp) ⟩ - map (flip lookupM (fromFunc (proj₁ wp))) t - ≡⟨ map-cong (lemma-lookupM-fromFunc (proj₁ wp)) t ⟩ - map (Maybe.just ∘ proj₁ wp) t - ≡⟨ map-∘ just (proj₁ wp) t ⟩ - map Maybe.just (map (proj₁ wp) t) ∎) ⟩ _ ∎) + ≡⟨ cong ((λ f → fmap f t) ∘ flip lookupM ∘ union h) (lemma-reshape-id g′) ⟩ + fmap (flip lookupM (union h g′)) t + ≡⟨ cong ((λ f → fmap f t) ∘ flip lookupM) (proj₂ wp) ⟩ + fmap (flip lookupM (fromFunc (proj₁ wp))) t + ≡⟨ IsFunctor.cong (isFunctor (|gl₁| i)) (lemma-lookupM-fromFunc (proj₁ wp)) t ⟩ + fmap (Maybe.just ∘ proj₁ wp) t + ≡⟨ IsFunctor.composition (isFunctor (|gl₁| i)) just (proj₁ wp) t ⟩ + fmap Maybe.just (fmap (proj₁ wp) t) ∎) ⟩ _ ∎) where open Get G - s′ = enumerate s - g = fromFunc (denumerate s) + s′ = enumerate ShapeT (|gl₁| i) + g = fromFunc (denumerate ShapeT s) g′ = delete-many (get s′) g - t = enumeratel (Get.|gl₁| G i) + t = enumerate ShapeT (|gl₁| i) wp = lemma-union-delete-fromFunc (lemma-assoc-domain (get t) v h p) data All-different {A : Set} : List A → Set where |